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5) In Problem 2, data on numbers of publications were given for an SRS of 50 faculty members. Not all departments were represented, however, in the SRS. The SRS contained several faculty members from psychology and from chemistry, but none from foreign languages. The following data are from a stratified sample of faculty, using the areas biological sciences, physical sciences, social sciences, and humanities as the strata. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 Number of Faculty Members in Stratum 1 2 102 310 217 178 0 1 0 807 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 10 2 0 Number of Faculty Members in Sample 1 2 1 1 0 9 0 1 0 2 0 1 0 0 7 19 13 11 8 2 0 1 0 0 0 0 0 50 Humanities a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. Note: For a frequency table, Y₁ = Σjesh fnjynj, and sh = -1 Σjesn fnj (Ynj — Yn) ². nh b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example.

5) In Problem 2, data on numbers of publications were given for an SRS of 50 faculty members. Not all departments were represented, however, in the SRS. The SRS contained several faculty members from psychology and from chemistry, but none from foreign languages. The following data are from a stratified sample of faculty, using the areas biological sciences, physical sciences, social sciences, and humanities as the strata. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 Number of Faculty Members in Stratum 1 2 102 310 217 178 0 1 0 807 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 10 2 0 Number of Faculty Members in Sample 1 2 1 1 0 9 0 1 0 2 0 1 0 0 7 19 13 11 8 2 0 1 0 0 0 0 0 50 Humanities a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. Note: For a frequency table, Y₁ = Σjesh fnjynj, and sh = -1 Σjesn fnj (Ynj — Yn) ². nh b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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5) In Problem 2, data on numbers of publications were given for an SRS of 50 faculty members. Not all departments were represented, however, in the SRS. The SRS contained several faculty members from psychology and from chemistry, but none from foreign languages. The following data are from a stratified sample of faculty, using the areas biological sciences, physical sciences, social sciences, and humanities as the strata. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 1 2 0 1 Number of Faculty Members in Stratum 2 0 1 0 102 310 217 178 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 807 Refereed Publications Faculty Members 10 2 0 1 0 28 DIINI 2 = Note: For a frequency table. Yn = —Σjesh fn¡Ynj, and s½ 2 = nh 1 4 0 2 Number of Faculty Members in Sample 0 1 0 0 0 7 8 2 0 1 931 0 0 0 0 11 a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. 50 Humanities b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications 1 nh-1 Σjesh fnj (Ynj - ÿn)². d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example. Problem 2. A university has 807 faculty members. For each faculty member, the number of refereed publications was recorded. This number is not directly available on the database, so requires the investigator to examine each record separately. A frequency table for number of refereed publications is given below for an SRS of 50 faculty members. 2 3 4 56 789 10 3 4 4 2 102 1
Transcribed Image Text:5) In Problem 2, data on numbers of publications were given for an SRS of 50 faculty members. Not all departments were represented, however, in the SRS. The SRS contained several faculty members from psychology and from chemistry, but none from foreign languages. The following data are from a stratified sample of faculty, using the areas biological sciences, physical sciences, social sciences, and humanities as the strata. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 1 2 0 1 Number of Faculty Members in Stratum 2 0 1 0 102 310 217 178 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 807 Refereed Publications Faculty Members 10 2 0 1 0 28 DIINI 2 = Note: For a frequency table. Yn = —Σjesh fn¡Ynj, and s½ 2 = nh 1 4 0 2 Number of Faculty Members in Sample 0 1 0 0 0 7 8 2 0 1 931 0 0 0 0 11 a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. 50 Humanities b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications 1 nh-1 Σjesh fnj (Ynj - ÿn)². d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example. Problem 2. A university has 807 faculty members. For each faculty member, the number of refereed publications was recorded. This number is not directly available on the database, so requires the investigator to examine each record separately. A frequency table for number of refereed publications is given below for an SRS of 50 faculty members. 2 3 4 56 789 10 3 4 4 2 102 1
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